Question

A segment of wire as shown in the figure carries a current 'I' and radius of the circular arc is ' \( R \) '. The magnitude of magnetic field at the geometrical centre \( (O) \) of the arc is 

(1) \( \frac{\mu_{0} I}{4 \pi R}\left(\frac{\pi}{2}+1\right) \) 

(2) \( \frac{\mu_{0} I}{4 R}\left(\frac{\pi}{2}+1\right) \) 

(3) \( \frac{\mu_{0} I}{4 \pi R}\left(\frac{\pi}{4}+1\right) \) 

(4) \( \frac{\mu_{0} I}{8 R}\left(\frac{\pi}{2}+1\right) \)

Answer 1

Magnetic At point A will be zero

B_A = 0

Magnetic at point B

B_B = \(\frac{\mu_0I}{4\pi R}.\frac{\pi}2\)

B_B = \(\frac{\mu_0i}{8 R}\)

Magnetic field at point C

B_C = \(\frac{\mu_0 i}{4\pi R}\)(sin 0° + sin 90°)

B_C = \(\frac{\mu_0 i}{4\pi R}\) 

Net magnetic field

B_net  = B_B + B_C

 = \(\frac{\mu_0i}{8 R}\) + \(\frac{\mu_0 i}{4\pi R}\) 

B_net = \(\frac{\mu_0 i}{4\pi R}\)(1 + \(\frac{\pi}2\))